Question

To find out the concentration of $S{O}_2$ in the air (in parts per million, i.e., ppm), the data was collected for $30$ localities in a certain city and is presented below:

Concentration of $S{O}_2$ (in ppm)	Frequency
$0.00-0.04$	$4$
$0.04-0.08$	$9$
$0.08-0.12$	$9$
$0.12-0.16$	$2$
$0.16-0.20$	$4$
$0.20-0.24$	$2$

Find the mean concentration of $S{O}_2$ in the air.

Answer 1

Concentration of $S{O}_2$ (In ppm)	Mid-value $\left(x_i\right)$	Frequency $\left(f_i\right)$	$f_i{x}_i$
$0.00-0.04$	$0.02$	$4$	$0.08$
$0.04-0.08$	$0.06$	$9$	$0.54$
$0.08-0.12$	$0.10$	$9$	$0.90$
$0.12-0.16$	$0.14$	$2$	$0.28$
$0.16-0.20$	$0.18$	$4$	$0.72$
$0.20-0.24$	$0.22$	$2$	$0.44$
Total		$30$	$2.96$

Let $\overline{x}$ be the required mean.

Mean, $\overline{x}=\frac{1}{n}\sum f_i{x}_i$

Here, $n=30,\sum f_i{x}_i=2.96$

Therefore, Mean, $\overline{x}=\frac{2.96}{30}=0.099$ ppm

We have used direct method because numerical values of $f$ and $x$ are small.